Answer: The Shulchan Aruch (OC 279:1) writes
that even after a candle has gone out on Shabbos, it remains muktze for
the rest of Shabbos. If one places their candles on a tray, the tray itself is
considered to be a bassis¸ a base, and is rendered muktze, too
(ibid. 309:4).
The Magen Avraham (277:8) and Shulchan Aruch Harav (OC 277:6;
310:16) write that if one places something such as challa on the bassis
before Shabbos comes in, then the table becomes a bassis for the
permissible item, too. This item must be more important than the muktze
item. In
this way, one would be able to move the bassis after the candles have
gone out (See Shulchan Aruch 310:8). The Mishna Berura (277:18) adds that it
must be an item that one needs for Shabbos. Thus, R’ Shlomo Zalman Auerbach
(quoted in Shemiras Shabbos Kehilchasa 20:n216) suggests placing a bottle of
wine on the table. R’ Shmuel Wosner (Shevet Halevi 8:52) explains that
this prominence does not mean that it is worth more, though dependent on its
necessity. As the challa or wine is needed for the Shabbos meal, it is
more important than the candles that are no longer burning.
In conclusion, if one wants to move the table after the menora
has gone out, one should place something important that one will later use such
as challos or wine on the table before Shabbos, thereby ensuring
that the table is not just a bossis for the muktze item.